Is the Nikon SB 900 compatible with the Nikon d3000?

Is it compatible wirelessly and do i need a trigger

Your D3000 can't control an off camera flash at all, you MUST put a flash controller in the hot shoe. Like an SB-900.

If you use cheap triggers, you will not have TTL control of the flash, and you $500 flash will be no more useful than a $50 manual flash. Of course TTL controllers and receivers are not cheap either, it would take another $500 to make that work.

You can use it on camera. If you want to use an off-camera flash, you'll need an SB900 and another off-camera flash, like the SB-900, or an SB-600

It will give you TTL and manual flash control when mounted in the hotshoe. IF you want to use it wirelessly, you have 3 choices;
- buy another Nikon speedlight that can act as a commander (SB800 - discontinued, but you can get them off eBay; SB700 or another SB900). This will then sit in the hotshoe & trigger the SB900 off camera. You will still have TTL and manual control off camera.
- buy an Nikon SU-800 IR trigger. This sits in the hotshoe, but is not a flash in itself, merely a trigger. It will trigger the SB900 off camera in TTL or manual mode
- buy a set of radio triggers (RF602's ar cheap AND good, at around £27).It will trigger the SB900 off camera, but in manual mode only, you'll not have TTL flash.

TTL flash is a kind of auto metering for flash - handy when you want to 'run & gun' with your shots, but can be unreliable at times - like all things Auto, it gets it wrong sometimes. Radio triggers will have more range & reliability, as unlike the Nikon system (CLS) they are not optically based.

Tbh, I wouldn't spend over £300 buying an SB900. I'd use the cash to get cheaper, manual speedlights plus some modifiers. For that amount you could rig yourself up a decent 2-3 light setup with light stands & softboxes/umbrellas.

Yes its a compatible to all nikon dslr

Nikon SB-900 AF Speedlight Flash for Nikon Digital SLR Cameras

High-quality flash for standalone use or as part of a comprehensive lighting system
Commander mode controls up to 3 Speedlight groups or unlimited individual Speedlights
4 wireless channel options; prominent master and remote control switch for wireless operation
Auto power zoom coverage ranges from 17 to 200mm (FX format) to 12 to 200mm (DX format)
3 light distribution patterns; measures 3 x 5.7 x 4.7 inches (W x H x D) and weighs 14.6 ounces